A338881 - OEIS

%I #6 Nov 14 2020 11:03:39

%S 1,1,2,3,4,5,6,7,1,1,2,3,4,5,6,7,2,2,4,6,8,10,12,14,3,3,6,9,12,15,18,

%T 21,4,4,8,12,16,20,24,28,5,5,10,15,20,25,30,35,6,6,12,18,24,30,36,42,

%U 7,7,14,21,28,35,42,49,1,1,2,3,4,5,6,7,1,1,2,3,4,5,6,7,2

%N Product of the nonzero digits of (n written in base 8).

%F G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7) * A(x^8).

%t Table[Times @@ DeleteCases[IntegerDigits[n, 8], 0], {n, 0, 80}]

%t nmax = 80; A[_] = 1; Do[A[x_] = (1 + x + 2 x^2 + 3 x^3 + 4 x^4 + 5 x^5 + 6 x^6 + 7 x^7) A[x^8] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%o (PARI) a(n) = vecprod(select(x->x, digits(n, 8))); \\ _Michel Marcus_, Nov 14 2020

%Y Cf. A007094, A051801, A117592, A309959.

%K nonn,base

%O 0,3

%A _Ilya Gutkovskiy_, Nov 13 2020